\relax 
\bibstyle{authordate1}
\@writefile{toc}{\contentsline {section}{\numberline {1}Problem Statement}{1}}
\newlabel{obs:relative}{{1}{1}}
\newlabel{obs:increasing}{{2}{1}}
\newlabel{obs:converging}{{3}{1}}
\newlabel{thm:main}{{1}{1}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Especial case of single AVF chance}{1}}
\newlabel{sec:especial}{{2}{1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Model parameters and the decision variable}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Objective function}{2}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces $L(u)$ and HD phases}}{2}}
\newlabel{fig:fig1}{{1}{2}}
\newlabel{eq:obj}{{4}{2}}
\citation{shaked2007stochastic}
\newlabel{pro:mainpro}{{1}{3}}
\newlabel{lem:bound}{{1}{3}}
\newlabel{lem:residual}{{2}{3}}
\newlabel{eq:obj2}{{6}{4}}
\newlabel{eq:obj3}{{7}{5}}
\newlabel{pro:stochf}{{2}{5}}
\newlabel{thm:AVFchance}{{2}{5}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Bridge to the multi-chance case}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces $X(u)$ for $u_1$ and $u_2$}}{6}}
\newlabel{fig:fig2}{{2}{6}}
\newlabel{pro:incr}{{3}{6}}
\newlabel{lem:sequence}{{3}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces $S(x)$}}{6}}
\newlabel{fig:fig3}{{3}{6}}
\newlabel{lem:ratio}{{4}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces possible cases for proposition 3\hbox {}}}{7}}
\newlabel{fig:fig4}{{4}{7}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces case 4 for proposition 3\hbox {}}}{8}}
\newlabel{fig:fig6}{{5}{8}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Multi-chance case}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Multi-chance recursive relation}}{8}}
\newlabel{fig:fig7}{{6}{8}}
\newlabel{eq:val}{{11}{9}}
\newlabel{thm:multi}{{3}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces caption}}{9}}
\newlabel{fig:fig8}{{7}{9}}
\bibdata{refs}
\bibcite{shaked2007stochastic}{{1}{2007}{{Shaked \& Shanthikumar}}{{}}}
\newlabel{lem:cond}{{5}{11}}
